{"id":"https://openalex.org/W2971626101","doi":"https://doi.org/10.1007/s10915-019-01041-x","title":"Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures","display_name":"Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures","publication_year":2019,"publication_date":"2019-09-06","ids":{"openalex":"https://openalex.org/W2971626101","doi":"https://doi.org/10.1007/s10915-019-01041-x","mag":"2971626101"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-019-01041-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-01041-x","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100621470","display_name":"Qiang Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Ma","raw_affiliation_strings":["School of Mathematics, Sichuan University, Chengdu, 610065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Sichuan University, Chengdu, 610065, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100704215","display_name":"Hao Wang","orcid":"https://orcid.org/0000-0003-2480-4436"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Wang","raw_affiliation_strings":["School of Mathematics, Sichuan University, Chengdu, 610065, China"],"raw_orcid":"https://orcid.org/0000-0003-2480-4436","affiliations":[{"raw_affiliation_string":"School of Mathematics, Sichuan University, Chengdu, 610065, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100781763","display_name":"Zhiqiang Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhiqiang Yang","raw_affiliation_strings":["Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070632878","display_name":"Zhihui Li","orcid":"https://orcid.org/0000-0002-8378-6269"},"institutions":[{"id":"https://openalex.org/I2802505932","display_name":"China Aerodynamics Research and Development Center","ror":"https://ror.org/00jma8s40","country_code":"CN","type":"facility","lineage":["https://openalex.org/I2802505932"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihui Li","raw_affiliation_strings":["Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang, 621000, China","National Laboratory for Computational Fluid Dynamics, BUAA, Beijing, 100191, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang, 621000, China","institution_ids":["https://openalex.org/I2802505932"]},{"raw_affiliation_string":"National Laboratory for Computational Fluid Dynamics, BUAA, Beijing, 100191, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057609561","display_name":"Junzhi Cui","orcid":"https://orcid.org/0000-0001-6422-2161"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junzhi Cui","raw_affiliation_strings":["LSEC, ICMSEC, Academy of Mathematics and Systems Science, CAS, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, CAS, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100781763"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6064,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.71373043,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"81","issue":"2","first_page":"689","last_page":"731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/axial-symmetry","display_name":"Axial symmetry","score":0.7557278275489807},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.6218849420547485},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5836367607116699},{"id":"https://openalex.org/keywords/electric-displacement-field","display_name":"Electric displacement field","score":0.5809483528137207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5764844417572021},{"id":"https://openalex.org/keywords/piezoelectricity","display_name":"Piezoelectricity","score":0.5548681020736694},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5129465460777283},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.49405625462532043},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.48958930373191833},{"id":"https://openalex.org/keywords/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.4837467670440674},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4448360800743103},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.43367132544517517},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3502679467201233},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3093325197696686},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28549179434776306},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.07348936796188354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07240217924118042}],"concepts":[{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.7557278275489807},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.6218849420547485},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5836367607116699},{"id":"https://openalex.org/C57470404","wikidata":"https://www.wikidata.org/wiki/Q371907","display_name":"Electric displacement field","level":3,"score":0.5809483528137207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5764844417572021},{"id":"https://openalex.org/C100082104","wikidata":"https://www.wikidata.org/wiki/Q183759","display_name":"Piezoelectricity","level":2,"score":0.5548681020736694},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5129465460777283},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.49405625462532043},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.48958930373191833},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.4837467670440674},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4448360800743103},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.43367132544517517},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3502679467201233},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3093325197696686},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28549179434776306},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.07348936796188354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07240217924118042},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-019-01041-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-01041-x","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4758542668","display_name":null,"funder_award_id":"11501389","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G560859918","display_name":null,"funder_award_id":"11801387","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6701505053","display_name":null,"funder_award_id":"11471214","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W170197162","https://openalex.org/W377201621","https://openalex.org/W597899981","https://openalex.org/W621751968","https://openalex.org/W650857255","https://openalex.org/W1515186765","https://openalex.org/W1547249381","https://openalex.org/W1553150814","https://openalex.org/W1964406827","https://openalex.org/W1966194794","https://openalex.org/W1966465080","https://openalex.org/W1968139237","https://openalex.org/W1968934867","https://openalex.org/W1972286568","https://openalex.org/W1975556426","https://openalex.org/W1982693592","https://openalex.org/W1988191468","https://openalex.org/W1990558817","https://openalex.org/W1991013658","https://openalex.org/W2006658358","https://openalex.org/W2012708562","https://openalex.org/W2013144138","https://openalex.org/W2018199261","https://openalex.org/W2027239222","https://openalex.org/W2029918260","https://openalex.org/W2044246363","https://openalex.org/W2056636213","https://openalex.org/W2062104481","https://openalex.org/W2068160021","https://openalex.org/W2083039855","https://openalex.org/W2097589604","https://openalex.org/W2107818936","https://openalex.org/W2119565718","https://openalex.org/W2127028574","https://openalex.org/W2129779507","https://openalex.org/W2136248989","https://openalex.org/W2138940269","https://openalex.org/W2153608804","https://openalex.org/W2157532773","https://openalex.org/W2184444950","https://openalex.org/W2191373195","https://openalex.org/W2313704895","https://openalex.org/W2315937409","https://openalex.org/W2574957115","https://openalex.org/W2592912235","https://openalex.org/W2594270184","https://openalex.org/W2596426160","https://openalex.org/W2606419305","https://openalex.org/W2782905811","https://openalex.org/W2797991124","https://openalex.org/W2798512682","https://openalex.org/W2808453668","https://openalex.org/W2947311164","https://openalex.org/W2951634824","https://openalex.org/W4241915449","https://openalex.org/W4293517935","https://openalex.org/W4300943935"],"related_works":["https://openalex.org/W1639593894","https://openalex.org/W63200814","https://openalex.org/W2367601375","https://openalex.org/W2371750680","https://openalex.org/W2360227361","https://openalex.org/W1999171692","https://openalex.org/W1600077717","https://openalex.org/W60226892","https://openalex.org/W2029022286","https://openalex.org/W4211215616"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-08T08:47:23.578185","created_date":"2025-10-10T00:00:00"}